Geometer's SketchPad_3D

We are studying HCI and user interface issues in the context of generating complex 3D geometry on a laptop computer. The special task used for this study is the generation of an interactive geometry editor that allows the construction of interesting isohedral tilings of 3D space analogous to the intricate designs by M. C. Escher in 2D. Because these tiles need to stack together seamlessly, moving any vertex on the tile surface will also force some other vertices in other domains of the tile surface to move; the computer is programmed to take care of these couplings and correlations. Challenges for the user interface arise from the fact that one would like to observe all changes occurring simultaneously on all sides of the tile, and from the fact that clusters of tiles typically occlude the interesting areas where they contact one another.